The height of two buildings is 34 m and 29 m respectively. If the distance between the two buildings is 12 m, find the distance between their tops.

Using the segment addition postulate approach, the valve of x is 7.

A postulate is a claim that is accepted as true in the lack of supporting data. Postulates serve as a basis for the verification of succeeding propositions and serve the dual purpose of defining concepts that are not yet specified. Two points determine a line segment. A line segment can go on for ever along a line.

The segment addition postulate states that if three points A, B, and C are parallel to one another in that sequence, then the lengths of AB and BC added together equal the length of AC.

AC = AB + BC

Substituting the given values, we get:

3x+3 = (-1 + 2x)+11

When the right side of the equation is simplified, we obtain:

3x + 3 = 2x + 10

Subtracting 2x from both sides, we get:

x + 3 = 10

Subtracting 3 from both sides, we get:

x = 7

Therefore, x = 7.

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Answer:

Step-by-step explanation:

Let's call the number of friends "f". Since each friend paid $12.75 for their meal, the cost of the meals can be represented as f * 12.75. And since each friend left the same amount for a tip, the cost of the tips can be represented as t * f.

The total cost of the dinner including the tip was $61, so we can write the following equation:

f * 12.75 + t * f = 61

Expanding the left side of the equation:

12.75f + t * f = 61

Combining like terms:

13.75f + t = 61

Solving for t:

t = 61 - 13.75f

So, the equation that describes the situation is t = 61 - 13.75f.

Answer:

Step-by-step explanation:

9.

f(x)=x²-10x+3

=x²-10x+25-25+3

=(x-5)²-22

vertex is (5,-22)

it has horizontal tangent at (5,-22)

or

f(x)=x²-10x+3

f'(x)=2x-10

it has horizontal tangent where 2x-10=0 or x=5

f(5)=5²-10(5)+3

=25-50+3

=-22

it has horizontal tangent at (5,-22)

If the x-values are equal for two points, then the two points are on a vertical line.

When there is a vertical line, then it will cross the x - axis at only a single point. This point will be such that all the x - values on the line would be  - values because the line stands on only one point on the x - axis.

The same applies to the y - axis for horizontal lines. This is because the horizontal line would cross the y - axis at a single point. For instance, all the points on y = 2, would have a y - value of 2.

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From the information given, there are 81 different possible outcomes if you spin 4 spinners labeled Red, Blue, Yellow.

A permutation is an arrangement of objects in a specific order, and spinning involves generating a random outcome from a set of possible outcomes.

When spinning the spinner, each outcome has an equal chance of occurring, so we can say that the set of possible outcomes is being randomly permuted.

Spinning can be thought of as a way to generate a random permutation of a set of possible outcomes.

Each spinner has three possible outcomes, so the total number of different possible outcomes for all four spinners is:

3 x 3 x 3 x 3 = 81

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Step-by-step explanation:

The transformation from the function f(x) = |x| to the function g(x) = |x| + 4 can be thought of as a vertical shift upward by 4 units. The shape of the absolute value function remains unchanged, but the entire graph is shifted upward along the y-axis by 4 units. This can be visualized by observing that for any value of x, g(x) = f(x) + 4.

So, the transformation of f(x) to g(x) is a vertical shift upward by 4 units

The given system of linear equations has a unique solution.

A linear equation is an algebraic equation in which each term has an exponent of 1 and when graphed, the result is always a straight line.

Given that, a system of linear equations, ​ y = 5x+1 and y = -2x-8, we are asked to find how many solutions do they have,

The rule for a system of linear equations, ​a₁x+b₁y+c₁ = 0 and a₂x+b₂y+c₂ = 0 are :-

​a₁ / a₂ ≠ b₁ / b₂, and the lines intersect at one only point.

a₁ / a₂ = b₁ / b₂ ≠ c₁ / c₂, and the lines are parallel.

a₁ / a₂ = b₁ / b₂ = c₁ / c₂, and the lines overlaps.

Checking for the given equations,

y = 5x+1 and y = -2x-8

Converting into standard form of the linear equations,

5x-y +1 = 0 and 2x+y+8 = 0

5/2 ≠ -1

The equation is following the rule of unique solution, also the graph is intersecting at one point, [graph is attached]

Hence, the given system of linear equations has a unique solution.

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Answer:

One solution

Step-by-step explanation:

On solving the provided question, we can say that the equation will be  distance = distance 36t + 18 = 63t distance = 63t = 63(2/3) = 42 miles

A mathematical equatiοn is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of twο mathematical expressions is known as an equation in algebra. Fοr instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relatiοnship between the two sentences οn either side of a letter is described by a mathematical fοrmula. Often, there is οnly one variable, which also serves as the symbοl. for instance, 2x – 4 = 2.

the equatiοn will be

distance = distance

36t + 18 = 63t

27t = 18

t = 18/27 = 2/3 hr

distance = 63t = 63(2/3) = 42 miles

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Now , to find the area

Total area of figure = Area of first Triangle + Area of second triangle

The area of the triangle = ( 1/2 ) x Length x Base

Total area of figure = ( 1/2 ) x ( 36 x 15 ) + ( 1/2 ) x ( 15 x 8 )

= ( 1/2 ) x 540 + ( 1/2 ) x 120

= 270 + 60

= 330 inches²

Therefore , the value is 330 inches²

Hence , The area of the figure is 330 inches²

The lengths of the pieces are 1ft and 9ft

From the information given, we have that;

The shorter side = x

The longer side of the board = 6 +3x

The total length = 10

Substitute the values, we have;

x + 6 + 3x = 10

collect the like terms

x + 3x = 10 -6

Add or substract the like terms, we have;

4x = 4

Now, make 'x' the subject of formula by dividing by 4, we get;

4x/4 = 4/4

x = 1 ft

The longer side = 9ft

Hence, the values are 1 and 9

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Answer:

Step-by-step explanation:

Statistical questions are questions that can be answered by collecting, analyzing, and summarizing numerical data. The data can then be used to make inferences, predictions, and draw conclusions.

In the context of statistical analysis, numerical data refers to data that can be measured and expressed as a number. For example, the number of hours someone spends practicing a musical instrument each week, or the number of books a student reads each month.

On the other hand, questions such as "Who is your favorite cartoon character?" cannot be answered with a number and therefore are not statistical questions. The answer to this type of question is qualitative or categorical data and can not be analyzed numerically.

It's important to note that while the questions that result in numerical data are often statistical questions, not all questions that result in numerical data are necessarily statistical questions. For example, the number of letters in someone's first name is a numerical piece of information, but it does not involve collecting and analyzing data to make inferences or draw conclusions.

Answer:2)How many hours do you practice your musical instrument each week.

Step-by-step explanation:

"How many hours do you practice your musical instrument each week?" is a statistical question that can result in numerical data.

This is a statistical question because it involves a numerical variable ("hours practiced per week"), which can be measured and quantified.

The probability that a randomly chosen college student exercises in the morning or afternoon is B. 0. 39.

The probability that a college student chosen at random will either exercise in the morning or afternoon can be found by the formula :

= Probability that student exercises in the morning + Probability that student exercises in the afternoon

Probability that student exercises in the morning = 0. 25

Probability that student exercises in the afternoon = 0. 14

The probability would therefore be:

= 0. 25 + 0. 14

= 0. 39

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The first equation 3(3x - 4) = 24 can be solved for x as follows:

3(3x - 4) = 24

9x - 12 = 24

9x = 36

x = 4

So, if Messi hit the target, he would score 4 points.

The second equation 6.8 (2.3x + 5.7) = 132.6 can be solved for x as follows:

6.8 (2.3x + 5.7) = 132.6

2.3x + 5.7 = 132.6 / 6.8

2.3x + 5.7 = 19.55

2.3x = 13.85

x = 6

So, if Ronaldo hit the target, he would score 6 points.

A. The value of cos 240° = [tex]\frac{-1}{2}[/tex]

B. The value of sin 240° = [tex]-\frac{\sqrt{3} }{2}[/tex]

What are basic Trigonometric functions?

The angles of sine,  cosine, and tangent are the primary classification of functions of trigonometry. And the three functions which are cotangent, secant, and cosecant can be derived from the primary functions. Basically, the other three functions are often used as compared to the primary trigonometric functions.

Part A:

we know that, cos (a +b)=cos a cos b - sin a sin b

cos 240° = cos (60° +180°)

=cos 60° cos 180° - sin 60° sin 180°

=[tex]\frac{1}{2} *(-1)-\frac{\sqrt{3} }{2} *0[/tex]

=[tex]\frac{-1}{2}[/tex]

Part B:

we know that, sin(a- b)=sin a cos b - cos a sin b

sin 240° = sin(270° - 30°)

=sin 270° cos 30° - cos 270° sin 30°

=[tex]-1 *\frac{\sqrt{3} }{2}-0*\frac{1}{2}[/tex]

=[tex]-\frac{\sqrt{3} }{2}[/tex]

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Their ages are 5 years, 25 years

Word problems are sentences describing a 'real-life' situation where a problem needs to be solved by way of a mathematical calculation.

Let L and Y represent the age of the older person and younger person respectively.

Using the given information, we can write:

L = 4Y + 5 --- (1)

L + Y = 30 --- (2)

From (2):

L = 30 - Y --- (3)

Put (3) in (1):

L = 4Y + 5

30 - Y = 4Y + 5

4Y + Y = 30 - 5

5Y = 25

Y = 25/5

Y = 5 years

Put Y = 5 into (3):

L = 30 - Y

L = 30 - 5

L = 25 years

Their ages are 5 years, 25 years

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The table of values is

X |f(x)

0 | 4

2 | 5.33

4 | 6.67

6 | 8

From the question, we have the following parameters that can be used in our computation:

y = 2x/3 + 4

We have the x values to be

x = 0, 2 4 and 6

Substitute the known values in the above equation, so, we have the following representation

y = 2 * 0/3 + 4 = 4

y = 2 * 2/3 + 4 = 5.33

y = 2 * 4/3 + 4 = 6.67

y = 2 * 6/3 + 4 = 8

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Answer:

9

Step-by-step explanation:

set up a ratio

20 is to 3x-2   as    ( 20 + 28) is to 7x -3

20 / ( 3x-2) = ( 20 + 28) / (7x-3 )           cross multiply to get

140x - 60 = 144x - 96

          36 = 4x

              x = 9

The missing operators in the equation are +, - and +,the equation should be -1080+379-(-3)+15=-683.

Two or more expressions with an Equal sign is called as Equation.

-1,080?379?-3?15=-683

We already have two negative operators (-1,080 and -3), so we need to use a positive operator to get the final result to be negative. We can achieve this by using the addition operator (+)

-1,080+379?-3+15=-683

-1080+394?-3=-683

-686?-3=-683

The missing operator should be negative to get the value -683

-686-(-3)=-683

-686+3=-683

Hence, the missing operators in the equation are +, - and +,the equation should be -1080+379-(-3)+15=-683.

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Grayson would need to invest approximately $10,994 to the nearest dollar for the value of the account to reach $15,000 in 5 years.

What is continuously compounded interest?

Continuous compounded interest indicates that an account balance is constantly earning interest and reinvesting that money so that it, too, earns interest.

The formula for continuous compounding is given by:

[tex]A = Pe^{rt}[/tex]

where A is the amount in the account after t years, P is the principal amount (the amount invested), r is the annual interest rate, and e is the base of the natural logarithm.

We want to find P when A = $15,000, r = 0.04, and t = 5 years.

Substituting these values into the formula, we get:

[tex]15000 =Pe^{0.04*5}[/tex]

Simplifying the right-hand side, we get:

[tex]15000 =Pe^{0.2}[/tex]

Dividing both sides by e^(0.2), we get:

[tex]P= \frac{15000}{e^{0.2}}[/tex]

Using a calculator, we get:

P ≈ $10,994

Therefore, Grayson would need to invest approximately $10,994 to the nearest dollar for the value of the account to reach $15,000 in 5 years.

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Answer:

Step-by-step explanation:

Cross-price elasticity of demand is a measure of the relationship between the prices of two goods and the quantity demanded of each. It is used to determine how changes in the price of one good affect the demand for another good.

In this scenario, Janet is shopping for formula and bottles for her baby. The price of her favorite brand of formula has increased by 20%, causing her to buy 50% fewer new bottles. The cross-price elasticity for the new bottles calculated using the cross-price elasticity formula is -2.5.

A negative cross-price elasticity value of -2.5 means that the two goods, formula and bottles, are complements. This indicates that an increase in the price of one good (the formula) leads to a decrease in the demand for the other good (the bottles). In other words, when the price of formula increases, Janet is less likely to buy as many new bottles because she is spending more on formula.

On the other hand, if the cross-price elasticity were positive, it would indicate that the two goods are substitutes. In that case, an increase in the price of one good (the formula) would lead to an increase in the demand for the other good (the bottles) as people switch to the cheaper alternative.

In summary, cross-price elasticity of demand is a useful tool for understanding the relationship between the prices of two goods and the quantity demanded of each, and can help businesses make informed decisions about pricing and product strategy.

The cross-price elasticity is -3.66., complements.

A demand that is elastic experiences a significant shift in quantity demanded as a result of a price adjustment. When the amount sought changes little as a result of a price adjustment, the demand is said to be inelastic.

The percentage change in the quantity demanded for one good has an impact on the percentage change in the price of another good, which is measured by the cross elasticity of demand.

Based on the values given above, the cross elasticity of demand will be:

= [(3 - 6) / (18 - 15)] × [(15 + 18) / (6 + 3)]

= (-3/3) × (33/9)

= -1 × 3.66

= -3.66%

Since it's a negative value, the goods are complement.

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Answer:

Step-by-step explanation:

The chef bought a total of 4 1/5 kilograms of beans.

Number of bags of beans the chef bought= 3

Quantity of beans in each bag = 1 2/5 kilograms

Total kilograms of beans bought by the chef= Number of bags of beans the chef bought × Quantity of beans in each bag

= 3 × 1 2/5

= 3 × 7/5

= 21/5

= 4 1/5 kilograms of beans

Ultimately, the chef bought 4 1/5 kilograms of beans.

Complete question:

a chef bought 3 bags of beans. Each bag contains 1 2/5 kilogram of beans. How many kilograms of beans did she buy?

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Answer: First, let's find out how many times a 100-pound person would take the antihistamine in a week:

Every 6 hours * 24 hours/day = 4 times a day

4 times a day * 7 days/week = 28 times a week

Next, let's find the number of 13.2 mg chewable tablets taken in a week:

A typical dose of 19 mg * 28 doses/week = 532 mg

532 mg / 13.2 mg/tablet = 40 tablets

So, a 100-pound person would take 40 chewable tablets in a week following the prescribed dosage.

Now, let's find the amount of liquid antihistamine to be taken in a week:

A typical dose of 19 mg * 28 doses/week = 532 mg

532 mg / 13.2 mg/10 mL = 40.15 mL

So, a 100-pound person would take 40.15 mL of liquid antihistamine in a week following the prescribed dosage.

Step-by-step explanation:

The scenarios can you reverse the dependent and independent variables while keeping the interpretation of the slope meaningful in

E) As the number of calls made by a cell phone increases, the cell phone bill amount increases.

We anticipate that independent variables will have an impact on dependent variables. What occurs as a result of the independent variable is referred to as a dependent variable.

Given:

We can see from Option A that the opposite may not be true, as an increase in the risk of lung cancer may not always be accompanied by an increase in the number of cigarettes smoked each day.

Now, second it is clear that the opposite may not be true because an infant's age may not necessarily increase along with his or her height.

Now, third also acknowledges that a rise in traffic is not always accompanied by an increase in pollution in a city.

Fourth, a rise in water density does not always imply an increase in the amount of salt present in the water.

Only in Option E do we find a potential reverse reliance because a rise in phone bill amount does typically correspond to a rise in cell phone call volume.

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Answer: The formula for exponential decay is given by:

P(t) = P0 * e^(-rt)

where P(t) is the profit at time t, P0 is the initial profit, r is the rate of decrease in percentage, and t is the time elapsed in years.

In this case, P0 = $9500, r = 0.9%, and t = 5 (the time elapsed from 2014 to 2019).

First, we need to convert the rate of decrease from a percentage to a decimal:

r = 0.9% / 100 = 0.009

Now, we can plug in the values into the exponential decay formula:

P(5) = $9500 * e^(-0.009 * 5) = $9500 * e^(-0.0455)

We can calculate the value of e^(-0.0455) using a calculator or mathematical software. The result is approximately 0.955.

Therefore, the profit in 2019 is:

P(5) = $9500 * 0.955 = $9027.25

So, the profit in 2019 would be $9027.25.

Step-by-step explanation:

Answer:If (x + 1) is a factor of the polynomial p(x), then p(x) can be written as:

p(x) = (x + 1) q(x)

for some polynomial q(x). By substituting x = -1 into this expression, we can find the value of c:

p(-1) = (-1 + 1) q(-1) = 0 q(-1) = 0

So,

0 = 5(-1)^4 + 7(-1)^3 - 2(-1)^2 - 3(-1) + c

= -5 + 7 - 2 + 3 + c

= c = 3

So, the value of c that makes (x + 1) a factor of the polynomial p(x) = 5x^4 + 7x^3 - 2x^2 - 3x + c is c = 3.

To give Tara a lower price, coupon 2 should be applied first.

A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.

Given:

Tara has two store coupons.

Coupon 1 gives her $10 off on one item.

Coupon 2 gives her 10% off on one item.

Tara can use both coupons together on one item in the store and choose which coupon to apply first.

For an item that has an original price of x dollars,

let f be the function that models the discount price of the item using only coupon 1,

and let g be the function that models the discount price of the item using only coupon 2.

The price of each item in this store is more than $20.

Let the price is $50.

So applying coupon 1 and then coupan2,

we get,

(50 - 10) - ($50 - $10) x 0.10 = $36

Now, apply coupon 2 and then coupon 1,

we get,

$50 x 0.10 - $10 = $35

Therefore, she should apply coupon 2 and then coupon 1.

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Answer:

If the base of the right rectangular prism is a square with sides that are 1/2 inch long, then the area of the base is (1/2)^2 = 1/4 square inches.

Since the volume of the prism is given as 3/8 cubic inches, we can use the formula for volume of a right rectangular prism (V = Bh) to solve for the height of the prism:

V = Bh

3/8 = (1/4)h

Multiplying both sides by 4, we get:

3 = h

So the height of the prism is 3 inches.

Therefore, the right rectangular prism has a square base with sides 1/2 inch long and a height of 3 inches, making it a 1/2 x 1/2 x 3 inch rectangular prism.